Sharp Bounds on the Distribution of the Hardy-Littlewood Maximal Function
نویسندگان
چکیده
منابع مشابه
A Sharp Estimate for the Hardy-littlewood Maximal Function
The best constant in the usual L norm inequality for the centered Hardy-Littlewood maximal function on R is obtained for the class of all “peak-shaped” functions. A function on the line is called “peakshaped” if it is positive and convex except at one point. The techniques we use include variational methods. AMS Classification (1991): 42B25 0. Introduction. Let (0.1) (Mf)(x) = sup δ>0 1 2δ ∫ x+δ
متن کاملOn the Variation of the Hardy–littlewood Maximal Function
We show that a function f : R → R of bounded variation satisfies VarMf ≤ C Var f, where Mf is the centered Hardy–Littlewood maximal function of f . Consequently, the operator f 7→ (Mf) is bounded from W (R) to L(R). This answers a question of Hajłasz and Onninen in the one-dimensional case.
متن کاملSharp Hardy-littlewood-sobolev Inequality on the Upper Half Space
There are at least two directions concerning the extension of classical sharp Hardy-Littlewood-Sobolev inequality: (1) Extending the sharp inequality on general manifolds; (2) Extending it for the negative exponent λ = n−α (that is for the case of α > n). In this paper we confirm the possibility for the extension along the first direction by establishing the sharp Hardy-Littlewood-Sobolev inequ...
متن کاملVector A2 Weights and a Hardy-littlewood Maximal Function
An analogue of the Hardy-Littlewood maximal function is introduced, for functions taking values in finite-dimensional Hilbert spaces. It is shown to be L bounded with respect to weights in the class A2 of Treil, thereby extending a theorem of Muckenhoupt from the scalar to the vector case. A basic chapter of the subject of singular integral operators is the weighted norm theory, which provides ...
متن کاملOn the Lp boundedness of the non-centered Gaussian Hardy-Littlewood Maximal Function
The purpose of this paper is to prove the L p (R n ; dd) boundedness, for p > 1, of the non-centered Hardy-Littlewood maximal operator associated with the Gaussian measure dd = e ?jxj 2 dx. Let dd = e ?jxj 2 dx be a Gaussian measure in Euclidean space R n. We consider the non-centered maximal function deened by Mf(x) = sup x2B 1 (B) Z B jfj dd; where the supremum is taken over all balls B in R ...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Proceedings of the American Mathematical Society
سال: 1963
ISSN: 0002-9939
DOI: 10.2307/2033819